What is the derivative of (e^{2x}/(x^2+1)) ?

The derivative of (e^{2x}/(x^2+1)) is (e^{2x}*2(x^2+1)-2xe^{2x})/((x^2+1)^2)

What is the first derivative of (e^{2x}/(x^2+1)) ?

The first derivative of (e^{2x}/(x^2+1)) is (e^{2x}*2(x^2+1)-2xe^{2x})/((x^2+1)^2)

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Popular >

\frac{d}{d x} (\frac{e ^{2 x}}{x ^{2} + 1})

\frac{e ^{2 x} \cdot 2 ( x ^{2} + 1 ) - 2 x e ^{2 x}}{( x ^{2} + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{2 x}}{x ^{2} + 1})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( e ^{2 x} ) ( x ^{2} + 1 ) - \frac{d}{d x} ( x ^{2} + 1 ) e ^{2 x}}{( x ^{2} + 1 ) ^{2}}

\frac{d}{d x} (e^{2 x}) = e^{2 x} \cdot 2

\frac{d}{d x} (x^{2} + 1) = 2 x

= \frac{e ^{2 x} \cdot 2 ( x ^{2} + 1 ) - 2 x e ^{2 x}}{( x ^{2} + 1 ) ^{2}}

\int_{0}^{1} e^{x} - x e^{x} d x

\int_{x}^{0.5} 8 d y

\frac{d}{d x} (\frac{x}{( x - 1 ) ^{2}})

1 + x, 0

x \to 1 lim (e^{6 x^{2} - 6 x})

What is the derivative of (e^{2x}/(x^2+1)) ?
The derivative of (e^{2x}/(x^2+1)) is (e^{2x}*2(x^2+1)-2xe^{2x})/((x^2+1)^2)
What is the first derivative of (e^{2x}/(x^2+1)) ?
The first derivative of (e^{2x}/(x^2+1)) is (e^{2x}*2(x^2+1)-2xe^{2x})/((x^2+1)^2)